Question

All chords of the curve 3x2 – y2 – 2x + 4y = 0 which subtend a right angle at the origin pass through a fixed point whose coordinates are

(a) (0,0)

(b) (1,-2)

(c) (1 + √10/3, -1)

(d) (2,-1)

Answer 1

Correct option**(b) (1,-2)**

Explanation :

See Fig. Let lx + my = 1 be the chord of the given curve subtending right angle at the origin: Suppose the line meets the curve at A and B. Hence, the combined equation of the pair of lines OA and OB is

3x2 - y2 - (2x - 4y)(lx + my) = 0

Since ΔAOB = 90°, from the above equation and from , we have

Coefficient of x2 + Coefficient y2 = 0

(3 - 2l) + (-1 + 4m) = 0

l - 2m - 1 = 0

l + m(-2) = 0

Hence the line lx + my = 1 passes through the point (1, 2).